CRYPTOLOGY (10 ECTS) Prerequisites: Algorithms and Complexity (DM508) or Groups and Vector Spaces (MM515) is recommended. A bachelor degree is required. Aims: The purpose of this course is to study cryptology, which is cryptography plus cryptanalysis - the creation of secret codes and the possibilities for breaking them. We will also study cryptographic protocols for the security of information. Many of the newer cryptosystems and cryptographic protocols are based on number theoretic problems, so these number-theoretic problems and algorithms for them will also be discussed in this course, as will some of the algebra necessary for understanding them. Cryptology has many applications, including sending private messages, enabling commerce over the Internet (through encryption of credit card numbers, electronic money, secure methods for electronic signatures on documents, etc.), authentication such as PIN codes for Dankort and logins, and secret sharing (requiring that k out of m people participate before some sensitive action can occur). Subjects covered: Classical cryptography, perfect secrecy, AES/Rijndael, public-key cryptography, RSA, secure hashing, signature schemes, secure hash functions, authentication, secret sharing, secure protocols, primality testing, factoring, discrete logarithms, selected relevant topics from algebra. Goals: After the course, the students should be able to 1. determine whether a symmetric or public key cryptosystem is appropriate for a given application 2. implement and analyze several cryptographic systems, functions, and protocols 3. implement and analyze techniques for breaking these cryptographic systems, functions and protocols 4. perform calculations relevant to the cryptographic systems, functions and protocols studied 5. prove that cryptographic systems, functions and protocols give the correct result and are secure/insecure 6. do simple proofs in algebra concerning concepts useful to the study of cryptosystems Evaluation: a) A 4 hour written exam where books, notes and calculators may be used. External examiner. Grades according to the 7-point marking scale. b) Homework assignments that count 3 ECTS of the 10 ECTS course total. Internal examination by the lecturer. Pass/Fail. The assignments must be passed in order to be admitted to the exam. Examination only when the course had been taught. Examination in other terms only after approval of the study board. Withdrawal date: Withdrawal from the exam must be 7 days before the first exam date. Course type: Lectures (42 hours) and exercises (42 hours). Teaching period: To be announced. Remarks: This course is taught in English.